U.S. patent number 6,191,515 [Application Number 09/389,913] was granted by the patent office on 2001-02-20 for combined passive magnetic bearing element and vibration damper.
This patent grant is currently assigned to The Regents of the University of California. Invention is credited to Richard F. Post.
United States Patent |
6,191,515 |
Post |
February 20, 2001 |
Combined passive magnetic bearing element and vibration damper
Abstract
A magnetic bearing system contains magnetic subsystems which act
together to support a rotating element in a state of dynamic
equilibrium and dampen transversely directed vibrations. Mechanical
stabilizers are provided to hold the suspended system in
equilibrium until its speed has exceeded a low critical speed where
dynamic effects take over, permitting the achievement of a stable
equilibrium for the rotating object. A state of stable equilibrium
is achieved above a critical speed by use of a collection of
passive elements using permanent magnets to provide their
magnetomotive excitation. In a improvement over U.S. Pat. No.
5,495,221, a magnetic bearing element is combined with a vibration
damping element to provide a single upper stationary dual-function
element. The magnetic forces exerted by such an element, enhances
levitation of the rotating object in equilibrium against external
forces, such as the force of gravity or forces arising from
accelerations, and suppresses the effects of unbalance or inhibits
the onset of whirl-type rotor-dynamic instabilities. Concurrently,
this equilibrium is made stable against displacement-dependent drag
forces of the rotating object from its equilibrium position.
Inventors: |
Post; Richard F. (Walnut Creek,
CA) |
Assignee: |
The Regents of the University of
California (Oakland, CA)
|
Family
ID: |
23540283 |
Appl.
No.: |
09/389,913 |
Filed: |
September 3, 1999 |
Current U.S.
Class: |
310/90.5 |
Current CPC
Class: |
F16C
32/0427 (20130101); F16C 27/00 (20130101); H02N
15/00 (20130101) |
Current International
Class: |
F16C
39/06 (20060101); F16C 39/00 (20060101); H02N
15/00 (20060101); H02K 007/09 (); F16C
032/04 () |
Field of
Search: |
;310/90.5 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
|
|
|
|
|
|
|
60-125414 |
|
Jul 1985 |
|
JP |
|
8-023689 |
|
Jan 1996 |
|
JP |
|
Primary Examiner: Tamai; Karl
Attorney, Agent or Firm: Thompson; Alan H.
Government Interests
The United States Government has rights in this invention pursuant
to Contract No. W-7405-ENG-48 between the United States Department
of Energy and the University of California for the operation of
Lawrence Livermore National Laboratory.
Claims
What is claimed is:
1. A magnetic bearing apparatus comprising:
an upper stationary element comprising a copper facing material
laminated to and beneath a disc-shaped soft iron plate;
at least one rotating member having a central axis of rotation and
at least one lower rotatable element magnetically connected to and
beneath said upper stationary element, said lower rotatable element
comprising soft iron and a permanent magnetic material fixedly
connected to and between portions of said soft iron, and
wherein said copper facing having a greater diameter than the
diameter of a soft iron facing on said rotatable element.
2. An magnetic bearing apparatus comprising:
an upper stationary element comprising a piece of conductive,
non-magnetic material connected to and beneath a piece of soft
magnetizable material; and
at least one rotating member having a central axis of rotation and
at least one lower rotatable element magnetically connected to and
beneath said upper stationary element, said lower rotatable element
comprising a second piece of soft magnetizable material and a piece
of permanent magnetic material fixedly connected to and between
portions of said piece of soft magnetizable material.
3. The apparatus defined in claim 2 wherein said upper stationary
element comprises a disc-shaped iron plate comprising copper or
aluminum laminated on the lower surface of said plate.
4. The apparatus defined in claim 2 wherein said lower rotatable
element comprising at least one concentric iron pole face embedded
with an annular ring comprising permanent magnet material.
5. The apparatus defined in claim 2 wherein said upper stationary
plate comprises a larger diameter than said lower ring and attract
each other.
6. The apparatus defined in claim 2 wherein said lower rotatable
element comprises tapered pole faces on said soft magnetizable
material.
7. The apparatus defined in claim 2 wherein said soft magnetizable
material comprises a polar face on said lower rotatable element
having concentric inner and outer pole faces.
8. An apparatus comprising:
at least one rotating member having a central axis of rotation and
at least one lower rotatable element magnetically connected to and
beneath an upper stationary element, said lower rotatable element
comprising a piece of soft magnetizable material and a piece of
permanent magnetic material fixedly connected to and between
portions of said piece of soft magnetizable material;
stabilization means for stabilization of said rotating member above
a critical angular velocity, wherein said means comprise a
plurality of elements comprised of stationary and co-rotating
parts, including said upper stationary element comprising a piece
of conductive, non-magnetic material connected to and beneath a
piece of soft magnetizable material;
said elements having force derivatives of such magnitudes and signs
that they together satisfy the requirement that:
the negative of the sum of the time averaged derivatives of the
force exerted between said stationary and said rotating part of
each element in the axial direction is greater than zero;
the negative of the sum of the time averaged derivatives of the
force between said stationary and said rotating part of each
element in the radial direction is greater than zero, but less than
that in said axial direction; and
the sum of the vertical forces exerted by the stationary elements
on the rotating elements is at least equal to the force of gravity
on said rotating elements and any other co-rotating elements to
which they are attached; and
means for sustaining said rotating member in stable equilibrium
until said rotating member has exceeded said critical angular
velocity.
9. The apparatus of claim 8, further comprising a vertical shaft
fixedly connected to said rotating member through said central axis
of rotation.
10. The apparatus of claim 8, wherein said rotating member is
positioned to utilize the force of gravity to suppress tilt
instabilities.
11. The apparatus of claim 9, wherein said stabilization means
comprise:
at least one radial stabilization element; and
at least one axial stabilization element.
12. The apparatus of claim 11, wherein said at least one radial
stabilization element comprises an attracting magnetic bearing
element comprising:
said upper stationary element comprising a disc-shaped iron plate
comprising copper or aluminum laminated on the lower surface of
said plate,
said lower rotatable element comprising at least one concentric
iron pole face embedded with an annular ring comprising permanent
magnet material,
and wherein said upper stationary plate and said lower ring have
different diameters and attract each other.
13. The apparatus of claim 11, wherein said at least one radial
stabilization element comprises a compound attractive magnetic
bearing element comprising:
said upper stationary element comprising a piece of copper
material, a piece of soft magnetizable material magnetically
connected to and above said piece of copper material, and a support
fixedly connected to said piece of soft magnetizable material;
and
said lower rotatable element magnetically connected to and beneath
said upper stationary element, said lower rotatable element
comprising:
a piece of soft magnetizable material having tapered pole faces,
and
a ring of permanent magnetic material wherein said ring is fixedly
connected to and between portions of said piece of soft
magnetizable material.
14. The apparatus of claim 11, wherein said at least one radial
stabilization element comprises an axially symmetric reduced
derivative attractive bearing element comprising:
a first element comprising:
a disc shaped iron structure having a central axis;
a plate of copper metal fixedly connected to the lower edge of said
disc-shaped iron structure; and
a second element comprising soft iron and a permanent magnet
material, further comprising a disc shaped structure having pole
faces disposed opposite said plate of copper metal.
15. The apparatus of claim 11, wherein said at least one radial
stabilization element comprises a reduced derivative,
attracting-type magnetic bearing element comprising:
a first element comprising:
a disc shaped iron structure;
a plate of copper or aluminum metal is fixedly connected to the
lower edge of said disc shaped iron structure; and
a second element comprising:
a disc shaped iron structure;
a permanent magnet material fixedly connected to and beneath said
disc shaped iron structure beneath;
and wherein the diameter of said first element is greater than the
diameter of said second element.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an improvement in magnetic
bearing/suspension systems for the near-frictionless support of
rotating elements, such as flywheels, electric motors and
generators and the like. More specifically, the invention is
directed to a special passive bearing element employed in a
dynamically stable, passive, totally magnetically energized
bearing/suspension system that does not require electrically
activated servo controlled systems to attain a stable equilibrium
at operating speed.
2. Description of Related Art
Motor and generator armatures, flywheel rotors, and other rotatable
components have conventionally been supported and constrained
against radially and axially directed forces by mechanical
bearings, such as journal bearings, ball bearings, and roller
bearings. Such bearings necessarily involve mechanical contact
between the rotating element and the bearing components, leading to
problems of friction and wear that are well known. Even
non-contacting bearings, such as air bearings, involve frictional
losses that can be appreciable, and are sensitive to the presence
of dust particles. In addition, mechanical bearings, and especially
air bearings, are poorly adapted for use in a vacuum
environment.
The use of magnetic forces to provide a non-contacting, low
friction equivalent of the mechanical bearing is a concept that
provides an attractive alternative, one which is now being
exploited commercially for a variety of applications. All presently
available commercial magnetic bearing/suspension elements are
subject to limitations, arising from a fundamental physics issue,
that increase their cost and complexity. These limitations make the
conventional magnetic bearing elements unsuitable for a wide
variety of uses where complexity-related issues, the issue of power
requirements, and the requirement for high reliability are
paramount.
The physics issue referred to is known by the name of Earnshaw's
Theorem. According to Earnshaw's Theorem (when it is applied to
magnetic systems), any magnetic suspension element, such as a
magnetic bearing that utilizes static magnetic forces between a
stationary and a rotating component, cannot exist stably in a state
of equilibrium against external forces, e.g. gravity. In other
words if such a bearing element is designed to be stable against
radially directed displacements, it will be unstable against
axially directed displacements, and vice versa. The assumptions
implicit in the derivation of Earnshaw's Theorem are that the
magnetic fields are static in nature (i. e. that they arise from
either fixed currents or objects of fixed magnetization) and that
diamagnetic bodies are excluded.
The almost universal response to the restriction imposed by
Earnshaw's Theorem has been the following: Magnetic bearing
elements are designed to be stable along at least one axis, for
example, their axis of symmetry, and then external stabilizing
means are used to insure stability along the remaining axes. The
"means" referred to could either be mechanical, i. e. ball bearings
or the like, or, more commonly, electromagnetic. In the latter
approach magnet coils are employed to provide stabilizing forces
through electronic servo amplifiers and position sensors that
detect the incipiently unstable motion of the rotating element and
restore it to its (otherwise unstable) position of force
equilibrium.
Less common than the servo-controlled magnetic bearings just
described are magnetic bearings that use superconductors to provide
a repelling force acting against a permanent magnet element in such
a way as to stably levitate that magnet. These bearing types
utilize the flux-excluding property of superconductors to attain a
stable state, achieved by properly shaping the superconductor and
the magnet so as to provide restoring forces for displacements in
any direction from the position of force equilibrium. Needless to
say, magnetic bearings that employ superconductors are subject to
the limitations imposed by the need to maintain the superconductor
at cryogenic temperatures, as well as limitations on the magnitude
of the forces that they can exert, as determined by the
characteristics of the superconductor employed to provide that
force.
The magnetic bearing approaches that have been described represent
the presently utilized means for creating a stable situation in the
face of the limitations imposed by Earnshaw's Theorem. The approach
followed by the first one of these (i.e., the one not using
superconducting materials) is to overcome these limitations by
introducing other force-producing elements, either mechanical, or
electromagnetic in nature, that restore equilibrium. The latter,
the servo-controlled magnetic bearing, is usually designated as an
"active" magnetic bearing, referring to the active involvement of
electronic feedback circuitry in maintaining stability.
Recently, U.S. Pat. No. 5,495,221, issued to Post (herein referred
to as "Post '221", has described what can be called a "passive"
magnetic bearing system. That is, a combination of stationary and
rotating elements that together achieve a stable state against
perturbing forces without the need for either mechanical,
diamagnetic, or electronically controlled servo systems.
Such a system differs fundamentally from previous prior art in that
it provides a magnetic bearing system (as opposed to a magnetic
bearing element) that can support a rotating object, and that
achieves a dynamically stable state, even though any one of its
elements, taken alone, would be incapable of stable static
levitation. The system described in Post '221 results in reduction
in complexity, together with concomitant increases in reliability,
reductions in cost, and virtual elimination of power losses that it
permits, relative to systems using servo-controlled magnetic
bearings.
However, a need still exists to improve such a system. The Post
'221 system employs axially symmetric passive levitating elements
energized by permanent magnets, and further employs special
stabilizer elements to overcome the limitations of Earnshaw's
theorem. Nevertheless, suppression of the effects of unbalance or
inhibition of the onset of whirl-type rotor-dynamic instabilities
driven by displacement-dependent drag forces are achieved in the
Post '221 system, if at all, by using vibration dampers that are
independently located and separate components from the levitating
and/or stabilizer elements.
SUMMARY OF THE INVENTION
The present invention provides a system that satisfies the
conditions required for a rotating body to be stably supported by a
magnetic bearing system as well as novel forms and combinations of
the elements of such a system that satisfy these conditions under
dynamic conditions, i.e., when the rotation speed exceeds a lower
critical value. The invention achieves a state of stable
equilibrium above a critical speed by use of a collection of
passive elements using permanent magnets to provide their
magnetomotive excitation.
The present invention is an improvement of the passive magnetic
bearing element described in the above-mentioned Post '221 patent
and incorporates a vibration damper within the passive magnetic
bearing element of the magnetic bearing system. The passive
magnetic bearing element includes (1) a novel upper stationary
element containing a disc-shaped soft iron plate laminated on its
lower surface with a relatively thin facing that is non-magnetic,
but highly conductive, e.g., a copper-containing facing, and (2) a
rotating element below the stationary element containing concentric
iron pole faces energized by an embedded ring of the permanent
magnet material. The dimensions of such a stationary element are
larger than the adjacent mating dimensions of the outermost pole
face of the rotating element so that the laminated thin facing
contributes a damping force for transversely directed vibrations.
Furthermore, the magnetic forces exerted by the collection of
elements including at least one of the novel stationary elements,
when taken together, levitate the rotating object in equilibrium
against external forces, such as the force of gravity or forces
arising from accelerations. At the same time, this equilibrium is
made stable against displacements of the rotating object from its
equilibrium position by using combinations of elements that possess
force derivatives of such magnitudes and signs that they can
satisfy the conditions required for a rotating body to be stably
supported by a magnetic bearing system over a finite range of those
displacements. More specifically, the larger dimensions of the
novel stationary element inhibit the generation of drag-producing
eddy currents from periodic fluxes developed in either the
stationary or rotating element(s).
The present magnetic bearing system contains at least two discrete
subsystems, at least one of which is energized by mobile
permanent-magnet material and the other by the laminated thin
facing stationary element. These subsystems, when properly disposed
geometrically, act together to support a rotating element in a
state of dynamic equilibrium. However, owing to the limitations
imposed by Earnshaw's Theorem, the present magnetic bearing systems
still do not possess a stable equilibrium at zero rotational speed.
Therefore, means are provided to hold the suspended system in
equilibrium until its speed has exceeded a low critical speed where
dynamic effects take over and thereby permit the achievement of a
stable equilibrium for the rotating object.
Because of the improved elements and characteristics it is expected
that magnetic bearing systems based on the present invention can be
employed in a variety of useful applications. These include, for
example, electromechanical batteries (modular flywheel energy
storage devices), high-speed spindles for machining, hard-disc
drive systems for computers, electric motors and generators,
rotating target x-ray tubes, and other devices where simplified
magnetic bearing systems can satisfy a long-standing practical need
for low-friction, maintenance-free, bearing systems.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a vertical-axis system.
FIG. 2a is a side view of a repelling magnetic bearing element.
FIG. 2b is a top view of the repelling magnetic bearing element of
FIG. 2a.
FIG. 3 is a graph of the diameter ratios between two ring
magnets.
FIG. 4a is a side view in cross-section of a compound attractive
magnetic bearing element.
FIG. 4b is a top view of the compound attractive magnetic bearing
element of FIG. 4a.
FIG. 5 is a plot of attractive force versus displacement.
FIG. 6a is a cross-sectional side view of an axially symetric
reduced derivative attractive magnetic bearing element.
FIG. 6b is a top view of the axially symetric reduced derivative
attractive magnetic bearing element of FIG. 6a.
DETAILED DESCRIPTION OF THE INVENTION
In the design of passive magnetic bearing systems in accordance
with the teachings of Post '221, which is incorporated herein by
reference in its entirety, it is necessary to use a combination of
passive elements with compensating force derivatives in order to
achieve stable levitation. One such element described in Post '221
is an upper stationary element(s) coupled with spring-like or
resilient material, or compliant and/or energy-dissipating supports
for the purpose of damping out oscillations of the rotating parts,
including whirl-type instabilities. The present invention relates
to an improved stationary element, preferably in disc form,
fabricated from a "soft" magnetizable material such as iron having
a relatively thin attached layer of non-magnetic, highly conductive
material such as copper or aluminum positioned adjacent to a
surface of the element that attracts the rotating part of the
system. Such a highly conductive thin layer on the stationary
element provides a single device with a dual-function, i.e.,
damping the whirl-type instabilities while still supporting (e.g.,
levitating) a rotating object. Through the nature of its design,
the dual-function device does not introduce displacement-dependent
drag forces that contribute to the generation of the whirl-type
instabilities. Although the present invention is directed to
improvements in the teachings of Post '221, describing the
embodiments of the present invention necessarily includes an
initial outline of the theoretical considerations that undergird
the operation of Post '221 as well as its disclosed elements.
As a starting point prior to discussing the present invention, the
conditions that must be satisfied in order for the suspended object
(for example, a flywheel rotor) to exist in a state of force
equilibrium will be defined. As an example, consider a
vertical-axis system such as is shown in FIG. 1. This figure shows
a rotor subjected to the force of gravity and to forces from a
bearing/suspension system, with the forces being shown as vectors.
Shaft 12 and rotor 13 are supported by an upper attractive bearing
comprised of a stationary component 10 and a rotating part 11, and
by a lower, repelling bearing composed of a rotating element 14 and
a stationary element 15. Not shown are the permanent magnet
elements within the bearing elements needed to energize them. In
the vertical direction the upward forces exerted by the top and
bottom bearing must sum up to the downward force of gravity.
Designating these vertical-acting forces as F.sub.vA (upper bearing
elements) and F.sub.vB (lower bearing elements), the equation for
vertical force equilibrium becomes:
where M is the mass of the rotor, and g is the acceleration of
gravity. Since the vertical force exerted by the bearing elements
depends on the axial position of the rotating element relative to
the stationary element, there will be a unique axial position of
the rotor where this equation can be satisfied (assuming sufficient
lifting power for the two bearings combined, of course).
For displacements at either end in the radial direction, the
condition for force equilibrium (assuming no lateral accelerations)
is simply that there be no net radial force exerted by the bearing
elements. For axially symmetric bearings this condition will be
automatically satisfied when the axis of the rotating element
coincides with the axis of the stationary element, as shown
schematically in FIG. 1. In this centered position (and only in
this position) any internal radial forces exerted, for example, by
magnets used in the bearing element will be exactly canceled.
While the above prescription, if followed, will assure that the
rotating elements (rotor plus rotating parts of the magnetic
bearing system) exist in a state of equilibrium against external
and internal forces, it does not say anything about whether this
equilibrium is a stable one. To achieve a stable state against
displacements from the position of force equilibrium it is
necessary to impose new constraints, in this case on the
derivatives of the forces themselves, that is, on the rates at
which the forces exerted by the bearing elements vary with
displacements from equilibrium. Thus, it will be necessary to
satisfy quantitative constraints on certain vector sums of these
derivatives for the plurality of bearing elements, acting in
concert. In order to satisfy these constraints it will be required
to employ special designs for each of the bearing elements, and the
teachings in Post '221 and herein provide unique magnetic bearing
elements that are capable of satisfying the quantitative
requirements on the force derivatives.
Before listing the equations defining the conditions under which
the bearing systems described herein are stable under displacements
from a position of force equilibrium, it is necessary to define the
nature of the displacements that must be considered. There are
three: The first is an axial displacement (up or down in the case
shown in FIG. 1). The second is a transverse displacement, without
tilting of the axis of rotation. The third is a symmetric tilt
about an axis that is perpendicular to the axis of rotation and is
located midway between the upper and lower bearing elements. It can
be seen that an arbitrary displacement can be described as a linear
combination of these three basic displacements.
A rotating system can be described as being supported stably
provided that a displacement from its equilibrium position in any
direction results in a restoring force that returns it to that
equilibrium position. The mechanical analogy is an object suspended
by pairs of tension springs that lie above and below, to the left
and right, and in front of and behind the object. As can be seen
intuitively, if the object is momentarily displaced in any
direction from its equilibrium position it will feel a restoring
force that will cause it to return to its equilibrium position
after transients have died out.
A mechanical tension spring has the property that the force it
exerts increases as it is stretched, in other words, that force can
be expressed (for small displacements) through a force derivative,
as follows:
where Dx is the displacement and dF/dx is the rate of change of the
force with displacement. It is common engineering practice to
represent the negative of the force derivative of springs by the
letter K, so that our equation can be written as:
where the subscript "x" refers to the spring constant for
displacements in the x direction. The minus sign in equation [3]
arises from the convention that a mechanical spring always operates
in a way to oppose the displacement, resulting in a force that is
directed oppositely to the displacement.
By analogy to the spring, the force derivatives of magnetic bearing
elements can be represented by values of constants K, with one
important difference: In the case of magnetic bearing elements
these constants may be either positive (forces anti-parallel to the
displacement, i.e., restoring forces) or negative (forces parallel
to the displacement). In fact, Earnshaw's Theorem tells us that any
simple magnetic bearing element, if it is restoring for one type of
displacement, say radial, will always be destabilizing for the
other displacement, here axial. From this fact follows the need for
servo control of conventional magnetic bearings. It is therefore
apparent that the use of a single simple magnetic levitating
bearing element, whether it be attractive (above the rotor in FIG.
1) or repelling (below in FIG. 1) cannot lead to a stable
equilibrium. As set forth herein, in order to achieve a stable
equilibrium using only passive elements (e.g. permanent magnets to
provide the magnetomotive force) it is necessary to use a
combination of elements, designed so that they together satisfy
prescribed quantitative conditions on their force derivatives.
It is the purpose herein to set forth quantitatively the conditions
required for a rotating body to be stably supported by a magnetic
bearing system and to show one or more unique designs and
combinations of the elements of such a system that satisfy these
conditions under dynamic conditions, i.e., when the rotation speed
exceeds a lower critical value.
Theoretical analyses of the conditions for positional stability of
a magnetically levitated rotating object yield the following
conditions:
For stability against displacements parallel to the axis of
rotation, it is required that: ##EQU1##
where K.sub.zj is the value of the spring constant (negative of the
force derivative) in the z (axial) direction for the jth bearing
element. The physics content of this equation is that it describes
the requirement that the net force derivative of the magnetic
bearing system should be positive, i.e. that there should exist a
net restoring force for displacements in the axial direction.
A necessary and sufficient condition for stability against radial
translational displacements (no tilt) is simply that: ##EQU2##
where K.sub.rj is the value of the spring constant (negative of the
force derivative) in the r (radial) direction for the jth bearing
element. It is clear from what has been said earlier that it is not
possible to satisfy both of these conditions with simple bearing
elements if j<2. It can also be shown that it is also impossible
to achieve better than a neutrally stable (i.e. incipiently
unstable) situation with simple passive elements even if
j.gtoreq.2. To achieve a truly stable state it is necessary to use
special elements, so designed as to achieve, together with the
other element or elements, the quantitative requirements imposed by
equations [4] and [5].
The satisfaction of the two equations, [4] and [5], will insure the
existence of an equilibrium that is stable against both axial and
radial-translational displacements. It may not, however, insure
stability against tilt-type displacements. There are two possible
avenues to insuring tilt stability, while at the same time
maintaining stability against the other two classes of
displacement.
The first way is to insure that, in equation [5], those values of
K.sub.rj associated with a given location (i.e. top or bottom in
FIG. 1) are net positive, i.e. if the K.sub.r value of one of the
two adjacent elements is negative in sign, then the K.sub.r value
of the other element must be positive and larger in magnitude than
the negative one. This condition will be satisfied in embodiments
of the invention that are described herein. A second way is to take
advantage of gyroscopic effects to stabilize an otherwise tilt
unstable system in which, even though equation [5] is satisfied,
one (or more) of the values of K.sub.rj is sufficiently negative
that the K values of two adjacent bearing elements (the bottom two
in FIG. 1) add up to a net negative value. In this case above a low
critical speed (which can be calculated theoretically, and which
can be made to lie below the intended operating speed range of the
rotating system) the system will be stable. Below that speed it
will be necessary (as it is in other embodiments to be described)
to use disengaging mechanical or other elements to keep the system
stable for speeds lower than the critical speed.
The invention herein and in Post '221 achieves a state of stable
equilibrium above a critical speed by use of a collection of
passive elements using permanent magnets to provide their
magnetomotive excitation. The magnetic forces exerted by these
elements, when taken together, levitate the rotating object in
equilibrium against external forces, such as the force of gravity
or forces arising from accelerations. At the same time, this
equilibrium is made stable against displacements of the rotating
object from its equilibrium position by using combinations of
elements that possess force derivatives of such magnitudes and
signs that they can satisfy the requirements implied by equations
[4] and [5] over a finite range of those displacements. In other
words, the inventive apparatus comprises at least one rotating
member having a central axis of rotation; magnetic means for
stabilization of the rotating member above a critical angular
velocity, wherein the magnetic means comprise a plurality of
elements comprised of stationary and co-rotating parts, the
elements having force derivatives of such magnitudes and signs that
they together satisfy the requirement that the negative of the sum
of the time averaged derivatives of the force exerted between the
stationary and the rotating part of each element in the axial
direction is greater than zero; the negative of the sum of the time
averaged derivatives of the force between the stationary and the
rotating part of each element in the radial direction is greater
than zero; and the sum of the vertical forces exerted by the
stationary elements on the rotating elements is at least equal to
the force of gravity on the rotating elements and any other
co-rotating elements to which they are attached; and means for
sustaining the rotating member in stable equilibrium until the
rotating member has exceeded said critical angular velocity.
In conventional magnetic bearing embodiments, the passive elements
are used, in various combinations, to achieve positional stability.
The design in that their configurations and structures is chosen so
as to satisfy the quantitative requirements on their force
derivatives that have been described previously.
FIGS. 2a and 2b depict a conventional repelling (levitating)
magnetic bearing element such as taught in Post '221 made up of two
annular rings made of permanent magnet material magnetized in the
directions shown. The magnetic bearing element is made of a
rotating upper element 20, and a stationary lower element 21. As
seen in the figures, the diameter of the upper ring is different
from that of the lower ring, and this difference in diameter is
preferred for its proper operation and distinguishes this repelling
bearing element from those used in previous magnetic bearing
systems. In the example shown, the upper ring 20 is the rotating
component, while the lower ring 21 is stationary. A theoretical
analysis of the repelling (vertical) force for this pair of rings
shows that the force is always repulsive, but that it has a maximum
value at a calculable height above the lower ring. In the centered
position shown the horizontally directed force is, of course, zero.
If one now calculates the derivatives of the force, both vertical
and horizontal, the following is found. At the point of maximum
vertical force the first derivative of the force is zero, both for
vertical and horizontal displacements with respect to that
position. Above that position the force derivative for vertical
displacements is negative (i.e. the K.sub.z value is positive),
corresponding to an axially stable situation. That is, a weight
equaling the repulsive force at that position would be stably
levitated, as far as vertical displacements are concerned. When the
value of K.sub.r at that same position is calculated, it is found
to be negative (radially unstable) and equal in magnitude to 50
percent of the value of K.sub.z. The negative sign is to be
expected from Earnshaw's Theorem; the factor of 2 reduction comes
from the circular average of the forces between the magnets. It is
important to note that if the diameters of the two magnets had been
the same, there would have been no maximum point in the repulsive
force at a finite vertical separation between the magnets, thus no
place where both the axial and radial K values vanished, or in the
vicinity of which they could be made small. To illustrate this
point, FIG. 3 shows the locus of points representing the diameter
ratios (horizontal axis) and vertical separations (vertical axis)
between two ring magnets, points where the force derivatives
approach zero. The curve shown is representative; for thicker rings
or different hole sizes somewhat different plots would result. It
should also be apparent that the desired property, i.e., the
achievement of control over the force derivatives by adjustment of
size and relative position of annular permanent magnet elements,
will also apply if the smaller of the two magnet elements fits
within the hole of the larger element, so that the two are nested
together. For this case the locus curve of zero force derivatives
will of course deviate from that shown in FIG. 3.
FIGS. 4a and 4b depict schematically a conventional compound
attractive magnetic bearing element such as taught in Post '221
comprised of upper stationary elements 25 and 26, wherein element
25 is fabricated from permanent magnet material, and element 26 is
fabricated from a "soft" magnetizable material such as iron. The
rotating parts of the bearing also include an element 28 made of
permanent-magnet material and an element 29 made of soft
magnetizable material. They are coupled mechanically with a spacer
30 made of non-magnetic material, such as aluminum. Upper element
26 is held in place by support 27, which couples to spring-like or
resilient material, not shown, for the purpose of damping out
oscillations of the rotating parts that are supported by lower
bearing elements 28, 29, and 30.
FIGS. 4a and 4b depicts an alternative method of achieving control
of the force derivatives through design. In these figures, two
equal-diameter permanent-magnet discs (or annular rings) are used.
In the gap between them disc- or washer-shaped iron pole pieces are
held in place by non-magnetic material supports. In operation one
of these disc pairs would be stationary, and the other one would be
attached to co-rotating elements, such as a flywheel rotor. By
adjusting the spacing of these discs relative to the
permanent-magnet elements, the attractive (or repulsive) force and
its derivatives can be controlled in order to meet design criteria.
Since the non-rotating iron pole piece need not be rigidly coupled
to its surroundings, it has been taught that it could be connected
to compliant and/or energy-dissipating supports to suppress
whirl-type instabilities. Because the mass of this pole piece is
designed to be less than the mass of its permanent-magnet exciter
assembly, it has been taught to be better able to respond to the
dynamic effects associated with whirl effects, and be better able
to suppress them.
FIG. 5 shows a plot of the calculated attractive force between a
systems such as is shown in FIGS. 4a and 4b. Over an appreciable
range of separations, the plot of attractive force versus
displacment is nearly flat, corresponding to a small, and
pre-determinable value of the axial force derivative.
The primary purpose of the special configurations just described
has been to provide a levitating permanent magnet bearing element
where the magnitude of the force derivatives can be adjusted in
order that this element, when taken together with other elements
described in Post '221 can satisfy the quantitative requirements
for positional stability embodied in equations [4] and [5].
The same theory that gave the analysis of the repelling pair of
magnets shown in FIGS. 2a and 2b also can give the force and force
derivatives for a case where the direction of magnetization of one
of the magnets is reversed, so that the pair becomes attractive. In
this case the position of zero derivative is the same as before,
but now the signs of the derivatives are reversed. For larger
separations K.sub.z is negative (unstable axially), while K.sub.r
is positive (stable radially). For smaller separations the
situation is again reversed, with the K values corresponding to
axial stability and radial instability. Again, the novel use of
different diameter magnet rings and the special choice of
separation distance allows control over the axial force of
attraction and its derivatives so as to, together with other
elements, satisfy the previously stated requirements for positional
stability of the rotating body.
In the design of attracting magnetic bearings for use in the
invention herein disclosed, and where it is desirable to utilize
the flux-directing property of iron pole faces, novel design
concepts which are herein claimed as a part of the invention, are
needed. FIGS. 6a and 6b are a schematic view (in section) of an
single axially assymmetric "dual-function" attractive magnetic
bearing element that provides means for stabilization of a rotating
member, particularly above a critical angular velocity, and also
for damping out oscillations of the rotating parts (e.g., damping
whirl-type instabilities). The stabilization means comprise a
plurality of elements comprised of stationary and co-rotating parts
such as a bearing element including an upper stationary element 30
and a lower rotatable element 32. Rotatable element 32 is usually
fixedly connected to a vertical shaft 48 of the rotating member
through its central axis of rotation (not shown). A typical
rotating member can be a rotor. The lower rotatable element can be
fabricated from a piece of soft magnetizable material 34 such as
iron and a piece of permanent magnetic material 36 fixedly
connected to and between portions of the piece of soft magnetizable
material 34. The representative rotatable element 32 has concentric
iron pole faces, including inner pole face 38 and outer pole face
40 which are energized by an embedded ring of permanent magnet
material 36 which can be of similar or equal diameter to that of
outer pole face 40. In some applications, the pole faces such as 38
and 40 can be tapered to increase the magnetic field at the gap, or
alternatively, grooves can be cut in such poles faces to produce a
concentric series of radially narrower poles. The effect of such
modifications in the pole faces of rotatable element 32 is to
increase the damping coefficient (described hereinafter) and/or the
attractive force between the stationary and rotatable elements.
The upper stationary element 30 contains a piece of highly
conductive, non-magnetic material 42, such as stainless steel,
titanium, aluminum or preferably copper, connected to and beneath a
piece of soft magnetizable material 44 (e.g., iron). Preferably,
highly conductive, non-magnetic material 42 can be fabricated to
completely cover the lower face 46 of soft magnetizable material
44. The diameter of upper stationary element 30 is substantially
larger than the diameter of outer pole face 40 of lower rotatable
element 32. The attraction occurs between upper stationary element
30 and the matching pole faces, for example pole faces 38 and 40.
FIG. 6b is an end view intended to show the circular nature of the
bearing element.
As a result of such relative dimensions between the stationary and
rotatable elements, the magnetic bearing element provides a lifting
force having a positive axial force derivative, but has a near-zero
radial force derivative. The presence of the highly conductive,
non-magnetic material (e.g., copper) facing 46 of piece 42 on
stationary element 30 also contributes a damping force for
transversely directed vibrations, particularly whirl-type
instabilities. Furthermore, facing 46 contributes essentially no
displacement-dependent azimuthally directed drag force due to the
axial symmetry of rotatable element 32 and the larger diameter of
stationary element 32. Thus, upon small fixed radial displacements
of rotatable element 32 from its normal axis of rotation, no
periodically varying fluxes are developed in either stationary
element 32 or rotatable element 30, consequently eliminating
essentially any drag-producing eddy currents.
The magnitude of the damping coefficient for the magnetic bearing
element can be predetermined from the integration, in the radial
direction, of the axial component of the square of the magnetic
field between the stationary and rotatable elements (B.sup.2.sub.z
rdr), multiplied by the thickness t of the highly conductive,
non-magnetic material facing (calculated in meters), and divided by
the resistivity p of the highly conductive, non-magnetic material
(calculated in ohm-m.). The expression is summarized as follows:
##EQU3##
Techniques known to those of ordinary skill in the art that
increase the damping coefficient and/or the attractive force
between the stationary and rotatable elements can be employed.
Changes and modifications in the specifically described embodiments
can be carried out without departing from the scope of the
invention, which is intended to be limited by the scope of the
appended claims.
* * * * *